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عنوان فارسی مقاله:
مدل های ریاضی برای مسائل بارگذاری چندین کانکتور
عنوان انگلیسی مقاله:
Mathematical models for multicontainer loading problems
سال انتشار : 2017
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بخشی از مقاله انگلیسی:
2. Previous work
There are not many papers that address the issues studied here, considering pallet and truck loading together. Following the typology for cutting and packing problems introduced by Wäscher et al. [4] the two problems, pallet and truck loading, can be classified as Single Stock Size Cutting Stock Problems. Morabito et al. [5] deal with the same problem but in two dimensions, because the products cannot be stacked. In a first phase, the problem consists in loading the maximum number of products on a pallet. They solve the problem by using the 5-block algorithm proposed by Morabito and Morales [6]. When the pallets are built, they use the same approach to load the pallets onto the trucks. Takahara [7] deals with the problem of loading a set of items on a set containers and pallets. A loading sequence for the items is chosen and it determines the order in which the items are inserted into the bins. The sequence is selected by a metaheuristic method based on a neighbourhood search. A selector determines the sequence of the bins. When a bin is selected, the first item is loaded into the bin, placing it in the first space in which it fits. If the item does not fit into the bin, the next bin is selected. A strategic procedure determines when to exchange the sequence of the items with a neighbour sequence and when the choice of the bin is changed from following the sequence to being randomly chosen, depending on the quality of the solutions. Moura and Bortfeldt [8] deal with the same problem in two steps. In the first step boxes are packed onto pallets, while in the second step these pallets are loaded into trucks. For packing boxes onto pallets they use the method proposed by Moura and Oliveira [9] and they deal with the problem of loading pallets into trucks as a one-dimensional bin packing problem, which is solved by a tree search procedure. The SCLP, in contrast, is a well-studied problem (see, e.g., Bischoff and Ratcliff [10], Araya and Riff [11], Zhu and Lim [12], Gonçalves and Resende [13,14], Araujo and Armentano [15], Fanslau and Bortfeldt [16], and Junqueira et al. [17]), where the real constraints that we are also facing received an increased attention. According to the survey by Bortfeldt and Wäscher [18], at least 13.9% of the container loading literature deals with weight limit, while weight distribution is considered by 12.1% of the papers. Gehring and Bortfeldt [19], Bortfeldt et al. [20], Terno et al. [21], and Egeblad et al. [22] are some of the authors who include weight limit constraints in their studies. Indeed, when the cargo is heavy, the weight becomes a very restrictive constraint, more than the volume or the space occupied. Weight distribution constraints require the weight of the cargo to be spread across the container floor, to avoid displacements during the journey or to balance the load between truck axles when the container is transported by truck. To achieve a good weight distribution, the center of gravity of the load should be in the geometrical mid-point of the container floor, as in Bischoff and Marriott [23], or should not exceed a certain distance from it, as in Bortfeldt and Gehring [24] and Gehring and Bortfeldt [19]. Axle weight is a constraint imposed by the means of transport and it has not been widely studied. Lim et al. [25] deal with a particular SCLP with axle weight constraints. They propose an integrated heuristic solution approach that combines a GRASP wall-building algorithm with ILP models. They first apply a customized wall-building heuristic based on the GRASP by Moura and Oliveira [9], including special considerations for box weight and density. Then they use an integrated approach to handle the weight requirements. If the container load limit is exceeded, they unload the necessary number of boxes by iteratively solving an ILP model to meet the requirement. If the axle weight limit is exceeded, they take two steps iteratively until the limit is satisfied: the first step consists in interchanging the positions of the walls created by the customized heuristic, whereas the second step consists in solving an ILP model to unload boxes and in applying one more time the first step to improve the container balance as well as to force a feasible weight distribution.
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کلمات کلیدی:
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